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I am trying to find the value of a bet, with my percentage, that some team will win to see if i think there is value in some bet. My question is, should i include the bookmakers margin, when i calculate the value of a bet, based on my percentage that some team will win?

I would think that i need to add the bookmakers margin to my percentage, to even out the margin they add to their odds -- is this wrong? Should i just go with my percentage and not add the bookmaker margin?

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    Right now the way you've worded this doesn't really have enough information for us to understand what you're asking. Can you give an example of this? Are you asking, given odds of +110 for a team, how you should evaluate the profit of a bet if you think they will win 55% of the time?
    – Joe
    Commented Jul 17, 2020 at 14:46
  • Lets say i have team 1 playing team 2. I think team 1 wins, with 60% probability. The odds is, lets say, 1.70. This means, that the bookmaker belive that the team will win (1/58,8%) of the time. If we add the rest of the bookmakers probabilities, we get: 5,6 and 3,65, which gives us: 1/5,6 = 17,9% and 1/3,65 = 27,4%. When i add these up, i get 104,1% total, so the bookmaker has a 4,1% markup. When i do my own percentages, should i then use my 60% (that i think the probability is), or should i use 60% + (4,1%/3) = 64,7%, adding the bookmakers markup, to my probability as well?
    – mbih
    Commented Jul 17, 2020 at 14:55
  • I think you need to explain what "do my own percentages" mean. You think it should be 60% to win, and then you're comparing to 1.7x payout, so 1.02 average payout - great, what's the question?
    – Joe
    Commented Jul 17, 2020 at 17:58
  • My question is at its core:how to find the value of a bet, meaning, is there value in the long run. Do i: 1. odds / my estimation (60% chance of victory) or 2. odds / my estimation (60% chance of victory) + bookmaker margin
    – mbih
    Commented Jul 18, 2020 at 9:00

2 Answers 2

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Fundamentally, you don't care what the bookie's margin is. If for a bet of X, your expected payout is 1.70X and the chance of winning is 0.60, then your expected payout is (0.60 * 1.70)X = 1.02X and you're in the money. Assuming your estimate of 0.60 is correct of course...

The only disclaimer here is to ensure that your payout is actually 1.70X; if you're in a jurisdiction which taxes betting in some way, be very careful as to whether the quoted odds are net of tax.

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  • Thanks for the answer. Can you elaborate on why?
    – mbih
    Commented Jul 20, 2020 at 15:09
  • Why what? So long as your expected payout is what you think it is, the maths is trivial. How odds are translated into expected payout is something that can vary between jurisdictions (e.g. whether the expected payout is gross or net of the bookie's odds) but once you've got your expected payout you're there.
    – Philip Kendall ♦
    Commented Jul 20, 2020 at 15:30
  • What i mean is: To the bookies chances, they add a margin. Why shouldnt i add the same margin, to even out their added margin?
    – mbih
    Commented Jul 20, 2020 at 17:42
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    That all depends on how things are presented. In the UK anyway, the bookie's margin isn't "added" to anything - their margin comes from the fact that $sum(p_outcome)$ over all outcomes where $p_outcome$ is the implicit probability of each outcome from the odds is more than one e.g. in a equally balanced contest, you'll see odds of something like 6/5 on for each side, giving $sum(p_outcome)$ = 6/11 + 6/11 = 12/11. Their margin is now that 1/11 "extra" which means the bookies make money even if they have equal bets on either side (continued...)
    – Philip Kendall ♦
    Commented Jul 20, 2020 at 17:56
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    However, as an individual better, you don't care about that. All you need to know is that your expected payout on a successful bet of X is 1.83X. If you also think that the match is a toss-up, you'll think your expected return is 0.5 * 1.83X = 0.92X and a bad deal. Other countries/areas may or may not include the bookie's margin in the published odds, but once you have the expected payout for a bet, you're good.
    – Philip Kendall ♦
    Commented Jul 20, 2020 at 18:03
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Let's elaborate more on why the simple (0.60 * 1.70)X expression gives you a value bet. Taking the same example as in Kendall's answer:

Expected-Profit = Prob.Win * Win-profit - Prob.Loss * Bet-amount

We have:

Prob.Win = 0.6       (this is your analysis)
Prob.Loss = 0.4      (this is your analysis)
Win-profit = 0.7     (this is the bookie offer)
Bet amount = 1.0     (this is your bet)

Plugging in we get:

Expected-Profit = 0.6 * 0.7 - 0.4 * 1.0

Noticing that:

Expected-Payout = Expected-Profit + Bet-amount

we have:

Expected-Payout = (0.6 * 0.7 - 0.4 * 1.0) + (1.0)
                = (0.6 * 0.7 - 0.4) + (0.6 + 0.4)
                = (0.6 * 0.7) + (0.6)
                = 0.6 * 1.7

and with this simplification we do not actually need to look at the prob. of other outcomes (loss or draw (draw not show in this example)) and can always express:

Expected-Payout = Prob.win * Win-Payout

where Prob.win is your calculated value, so any Expected-Payout > 1.0 is in the money (in this case 0.6 * 1.7 = 1.02).

The same analysis can be done on other bets (loss or draw).

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